If a reaction follows the Arrhenius equation, the plot lnk vs 1/RT gives a straight-line having intercept 'In a' unit on positive y-axis. The maximum value of rate constant k is :

Options

A. `-a` unit
B. a R unit
C. a unit
D. a/R unit

Explanation

To solve the problem, we will use the Arrhenius equation and analyze the relationship between the rate constant \( k \) and temperature \( T \).

### Step-by-Step Solution:

1. **Understand the Arrhenius Equation**:
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = pre-exponential factor (frequency factor)
- \( E_a \) = activation energy
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

2. **Take the Natural Logarithm**:
Taking the natural logarithm of both sides gives:
\[ \ln k = \ln A - \frac{E_a}{RT} \]

3. **Rearranging the Equation**:
We can rearrange this equation to match the form of a straight line \( y = mx + c \):
\[ \ln k = -\frac{E_a}{R} \cdot \frac{1}{T} + \ln A \]
Here, we can identify:
- \( y = \ln k \)
- \( x = \frac{1}{T} \)
- \( m = -\frac{E_a}{R} \) (slope)
- \( c = \ln A \) (y-intercept)

4. **Identify the Maximum Value of \( k \)**:
The maximum value of \( k \) occurs when the term \( -\frac{E_a}{RT} \) is minimized. This happens when \( T \) approaches infinity (as \( R \) is constant).

5. **Limit as \( T \to \infty \)**:
As \( T \) approaches infinity:
\[ \frac{1}{T} \to 0 \]
Therefore, the equation simplifies to:
\[ \ln k = \ln A \]
This implies:
\[ k = A \]

6. **Conclusion**:
The maximum value of the rate constant \( k \) is:
\[ k_{\text{max}} = A \]

### Final Answer:
The maximum value of the rate constant \( k \) is \( A \).